If torque is calculated relative to a reference point and this point is displaced,does the condition for rotation remain valid?

Can a body remain in partial equilibrium? Explain with an illustration.

$A$ uniform rod $AB$ of length $\ell$ and mass $M$ is suspended from a point at a variable distance $x$ from end $A$,as shown. To keep the rod horizontal,a mass $m$ is suspended from its end $A$. $A$ set of $(m, x)$ values is recorded. The appropriate variables that give a straight line when plotted are:

$A$ uniform meter scale balances at the $40\,cm$ mark when weights of $10\,g$ and $20\,g$ are suspended from the $10\,cm$ and $20\,cm$ marks. The weight of the meter scale is ...... $g$.

$A$ metre scale is balanced on a knife edge at its centre. When two coins,each of mass $10\, g$,are placed one on top of the other at the $10.0\, cm$ mark,the scale is found to be balanced at the $40.0\, cm$ mark. The mass of the metre scale is found to be $x \times 10^{-2}\, kg$. The value of $x$ is

$A$ metre scale is supported on a wedge at its centre of gravity. $A$ body of weight '$W$' is suspended from the $20 \text{ cm}$ mark and another weight of $25 \text{ g-wt}$ is suspended from the $74 \text{ cm}$ mark to balance it, and the metre scale remains perfectly horizontal. Neglecting the weight of the metre scale, the weight of the body is: (in $\text{ g-wt}$)